Recoil can be calculated using a math formula that involves 4 things.
The guns weight. Less weight, more recoil
The weight of the projectile. Less weight, less recoil.
The powder charge. Less powder, less recoil
Muzzle velocity. Less velocity, less recoil.
http://www.handloads.com/calc/recoil.asp
If you know all the information you can plug in the numbers here and find out.
Changing any 1 factor can effect recoil. By shortening the barrel, you are getting less velocity, so less recoil. You are also making the gun lighter, so that means more recoil.
Personally I think it is pretty close to an even tradeoff. It is possible that your gun does recoil slightly less with the same loads you were shooting before, but I'd think the difference would be hard to detect.